Fading channels result from time-varying multipath reflections or scattering of a transmitted signal so that multiple signal versions with different delays, amplitudes, and phases arrive simultaneously at the receiver. Multipath amplitude and phase values combine at certain frequencies resulting in signal enhancement while at other frequencies cancellation occurs. Consequently the signal response across the frequency band is not constant as occurs when there is no multipath. The fading due to this effect is then described as frequency dispersive. In single carrier systems where data is sent in a serial stream of modulated symbols, the frequency dispersive fading in high data rate applications causes interference between symbols, i.e., intersymbol interference (ISI), that seriously degrades the bit-error rate if the ISI effect is not taken into account. The time variation of the multipath effects produces corresponding time variations in received signal strength. This aspect of fading is termed time dispersive. The time variation is unknown so that an adaptive receiver is required. Frequency and time dispersive fading are found in radio systems such as High Frequency (HF) ionospheric scatter, diffraction line-of-sight (LOS), mobile phone cellular, wireless local area network (WLAN), and tropospheric scatter. One type of protection against fading is accomplished by sending the same data on parallel channels that exhibit decorrelated fading. The parallel channels are called diversity channels and the number of available parallel channels is called the diversity order.
The channel multipath resulting in frequency dispersive fading produces in single carrier (SC) systems a form of redundant signal paths that fade independently. An adaptive equalizer can combine these redundant signal paths producing a form of implicit diversity protection against fading. The adaptive equalizer also minimizes the ISI resulting from the multipath. Consequently there is both an implicit diversity gain and an ISI penalty associated with these equalizer functions. In radio channel applications the ISI penalty is usually small and the performance of the equalizer is typically close to that of an ideal matched filter that coherently combines all the multipath contributions. Alternatively a multicarrier (MC) system often referred to as orthogonal frequency division multiplexing (OFDM) can achieve high data rates by apportioning the bits to be transmitted among a plurality of subcarriers each of which uses a symbol length that is long compared to the multipath delay spread. The small amount of ISI that results is eliminated by a time gate function. This gate function can be realized, for example, by sending no signal during the gate or by repeating previously transmitted data in a cyclic index technique. The MC technique is used in multiuser systems such as WLAN applications with one-to-many or many-to-one configurations. In radio systems where nonlinear power amplifiers are used, there is a significant loss in MC systems associated with backing off the power amplifier by a peak-to-average ratio to ensure linear operation. The combination of the time gate loss and peak-to-average ratio in MC systems is significantly larger that the combination of ISI penalty and peak-to-average ratio loss in adaptive equalizer SC systems. Consequently in long distance radio applications adaptive equalized SC systems are preferred because power amplifier size and cost dominate the design choice. However, in indoor or short-distance WLAN applications OFDM is used because the adaptive equalizer and its associated complexity can be omitted and power amplifier limitations are not as important.
Tropospheric scatter (or “troposcatter”) systems represent an important present application of duplex radio links containing fading dispersive channels. A troposcatter radio link exploits inhomogeneities in the troposphere resulting in scattered signals that can be received at distances beyond the radio horizon. The scatter mechanism is compensated by utilizing parallel transmission paths, i.e. diversity channels, which contain the same transmitted data but fade independently. Conventional systems would typically use quadruple diversity corresponding to a combination of dual transmit diversity using two separate frequency bands sending the same data on each of the frequency bands and dual receive diversity using two receiver antennas. Additional diversity provided by system design is termed explicit diversity as opposed to implicit diversity that results from channel multipath associated with the fading dispersive channel. Troposcatter systems may include multiple duplex links for purposes of providing digital data trunks containing digitized voice data and digital data including computer data and Internet traffic. These digital troposcatter systems are used in commercial applications, for example, for providing communication to oil drilling platforms at sea, and in military applications in both tactical and strategic configurations. Although many digital troposcatter systems were replaced by satellite technology in the 80's and 90's, the utility of rapid development of tactical systems and the cost and availability of satellite lease service are factors contributing to the continuing use of digital troposcatter systems. Tropospheric Scatter Communications by P. Monsen in Wiley Encyclopedia of Telecommunications, John Wiley & Sons, New York, N.Y., provides a summary and implementation considerations for this radio system technique.
In the 1970 time frame, adaptive equalization in single carrier systems was developed to combat the time-varying multipath effects associated with dispersive fading channels resulting in a data rate increase of about a factor of ten in digital troposcatter applications. This increase was due to the exploitation of the multipath in the form of implicit diversity channels as opposed to previous systems that attempted to minimize the multipath effects. An optimum infinite length decision-feedback equalizer (DFE) and a practical adaptive realization were described in Feedback Equalization for Fading Dispersive Channels, P. Monsen, IEEE Trans. on Information Theory, pp. 56-64, January 1971. A DFE modem based on these principles was developed and operated at a maximum data rate of 12.6 Mb/s in a 99% bandwidth of 15 MHz and was subsequently used in strategic troposcatter links. See C. J. Grzenda, D. R. Kern and P. Monsen, Megabit Digital Troposcatter Subsystem, (hereafter MDTS) NTC Conference Record, New Orleans, December 1975, pp. 28-15 to 28-19. Performance of a digital modem is typically characterized by an average bit-error rate as a function of a received signal-to-noise usually expressed as the ratio of average received energy per bit Eb to noise spectral density N0. In channel simulator tests in a quadruple diversity configuration the DFE modem was shown to provide an average bit error rate of 1E-5 at an Eb/N0 of 10 to 12 dB per diversity (16 to 18 total Eb/N0) for 12.6 Mb/s over a multipath range of two-sigma values from 30 to 300 nanoseconds. See FIG. 4 in Theoretical and Measured Performance of a DFE Modem on a Fading Multipath Channel, P. Monsen, IEEE Trans. on Comm., October 1977. In the discussion to follow the mean Eb/N0 per diversity value of 11 dB is used as a troposcatter link design objective.
In U.S. provisional patent application No. 60/653,225 Technique for Adaptive Equalization in Band-Limited High Data Rate Communication over Fading Dispersive Channels, (hereafter Adaptive Equalization and incorporated by reference) which provides a domestic priority for U.S. Ser. No. 11/348,816 file Feb. 6, 2006, now U.S. Pat. No. 7,590,204 issued Sep. 15, 2009, an optimum finite-length DFE is described for a spectrally efficient high data rate application. Rather than estimating the equalizer parameters as in MDTS, this DFE is adapted by estimating the channel using reference data that has been transmitted with digital data information and is locally available at the receiver. The DFE parameters are then computed directly from the channel parameters. With advances in technology and the optimum finite-length structure, a DFE modem based on the principles of Adaptive Equalization would be able to operate at higher data rates than MDTS under the same channel conditions.
Unfortunately the data rate of 12.6 Mb/s achieved in the 1970's in troposcatter systems has not been further improved with more powerful equalizers such as described in Adaptive Equalization because digital troposcatter systems are power limited. Existing systems use antennas and power amplifiers that are near practical limits for data rates on the order of 10 Mb/s. Troposcatter links are characterized by their annual median path loss L (50%) and a variable loss Y (q %) that accounts for variation in the hourly median values of path loss. The diurnal, monthly, and seasonal variations in received signal are an important characteristic of these radio links and results in a data rate limitation. In Troposcatter Radio Links (hereafter Radio Links), by G. Roda, Artech House, Boston, Mass. 1988, methods of prediction of troposcatter loss parameters are summarized. In one example in Table 6.2 of Radio Links, a 366.8 km path operating at 2.7 GHz is predicted to have a 214.4 annual median path loss. Troposcatter systems are commonly designed for an availability of q=99.9% corresponding to a worst case performance exceeded in only 8.76 hours of the year. Variability losses are detailed for different climate types in Fig. 6.3 of Radio Links. For a continental temperate climate (type 6) the variability loss for q=99.9% is seen to vary from 12 to 24 dB over a practical range of distances. Converting path loss into an Eb/N0 per diversity value requires an additional calculation of gain loss resulting from the use of narrow beam antennas that illuminate only part of the useable scattering volume. Using Eq. 4.6 in Radio Links and a 99.9% value of 18 dB for variability loss from Fig. 6.3e, a calculation for a 12.6 Mb/s shows that a mean 11 dB Eb/N0 per diversity can be achieved on this quadruple diversity 366.8 km path with two 8.5 meter antennas at each link end with each antenna at the link end having a power amplifier of 1.6 kw.
Because of limitation of available bandwidth in the S-band (1.55 to 5.2 GHz) region, the feasibility of utilizing frequencies in the Ku-band (10.9-17 Ghz) around 15 GHz for troposcatter communication has been under investigation. See 5-15 GHz Scattering Study, AD A236 350, R. Crane, Rome Lab., NY 13441, May 1991. Because of the troposcatter power limitation as seen in the previous discussion, the advantages of additional bandwidth could not be used to significantly increase the data rate. Instead additional bandwidth could be used to increase the combination of explicit and implicit diversity either through frequency hopping or direct-sequence spreading of the transmitted signal. These techniques would lower the required Eb/N0 by a few dB which could be used to offset transmission losses in this higher frequency band and/or reduce antenna/power amplifier parameters.
Although present troposcatter systems are considered to be power limited, information theory calculations show that this not need be the case. In the R=12.6 Mb/s example given above there are two transmitted frequency channels each occupying a bandwidth of 15 MHz. The 12.6 Mb/s is an uncoded system with a normalized information rate r=R/W=0.84 for each of the two transmit frequency channels. In the conventional diversity system the same data is transmitted on each of the two transmit frequency channels. With capacity-achieving codes one can send independent data on each of the two transmit frequency channels so the Shannon capacity formula for normalized capacity C/W isc=C/W=DT log2(1+P/N0W)  (1)
where DT is the order of transmit diversity and P is the received signal power and N0 is the noise spectral density. The ratio of energy per bit Eb to noise spectral density is given by
                                          E            b                                N            0                          =                              P                          RN              0                                =                      P                                          rN                0                            ⁢              W                                                          (        2        )            
For a mean 11 dB Eb/N0 per diversity in a 2S/2F configuration there is 14 dB Eb/N0 available for each of the DT=2 transmit channels. The signal-to-noise ratio per Hz (SNR/Hz) per transmit diversity for a rate of 0.84 is 13.2 dB and the normalized capacity from Eq.(1) is 8.92 bits/second/Hz, i.e. 10.6 times faster than the 1970's 12.6 Mb/s system. A troposcatter system operating at 134 Mb/s will certainly require more powerful equalization but signal processing power to realize such equalization has enormously increased in the last 30 years. According to Moore's law of doubling every 1.5 years the processing gain is a factor of 220=1,048,576.
However the Shannon channel capacity applies to memoryless channels wherein received symbols have independent and identical statistics. A fading dispersive channel is not a memoryless channel due to frequency selective and time selective fading effects. Frequency selective fading produces multipath induced intersymbol interference (ISI) that causes the received symbols to be statistically dependent and not independent. Time selective fading produces correlation between received symbols. Fading dispersive channels can be converted into memoryless channels over an interval by using interleaving techniques but the associated delay is unacceptable in most practical applications.
A present or future radio system that includes fading dispersive channels will increasingly handle Internet Protocol (IP) traffic instead of a high speed digital data trunk containing a mixture of digitized voice and computer data. In previous systems the data rate associated with the digital data trunk was fixed so that if communication conditions improved there was no mechanism for exploiting the improved conditions. Further as noted above previous systems commonly used a criterion of average bit error rate in the system design. The average would be taken over many fading intervals. Packets sent using Internet Protocol may be retransmitted if a certain quality level is not achieved. In voice IP transmissions (VOIP) the packets are not retransmitted but a certain quality level corresponding to the maximum number of error bits in the packet, i.e., an outage probability, is important. Consequently data rate throughput and outage probability are criteria of importance in the IP systems.
Fading dispersive channels in duplex (opposite directions simultaneously) applications are almost always not reciprocal, i.e., the channel conditions are not the same in both communication link directions. This lack of reciprocity arises from the need to separate transmit and receive frequencies at a single terminal end. Since transmission and reception is not on the same frequency, the frequency selective fading in the dispersive channel will preclude reciprocity.
Feedback communication can be used on communication links that are not reciprocal in order to relate back to the transmitter the quality of reception at the distant terminal. Practical feedback communication techniques must cope with transmission delay, time variation of the channel, error in quality assessment at the receiver, potential errors in the feedback message, and additional overhead to support quality assessment and the feedback message. Although it is well known that feedback communication does not increase the channel capacity on memoryless channels, one can construct examples of channels with memory whose capacity is increased by feedbacks, see Coding for Channels with Feedback, J. M. Ooi, Kluwer Academic Publishers, Boston, Mass. 1998, pg. 4 and section 3.5.2. Feedback communication using a return communications channel is commonly used in the initial selection of transmitted data rate as part of the establishment of a digital data channel. In U.S. Pat. No. 5,999,563, Rate Negotiation for Variable-Rate Digital Subscriber Line Signaling, the modem negotiates for a desired line transmission rate to accommodate line conditions. Protocol messaging is used to provide feedback communications and bandwidth selection in a cable application in U.S. Pat. No. 6,223,222, Method and System for Providing Quality-of-Service in a Data-over-Cable System with Protocol Messaging. Feedback communications to determine transmitted power levels are described in U.S. Pat. Nos. 6,853,675 and 6,298,220. In U.S. Pat. No. 5,475,711, System for Channel Capacity Modulation, the signal-to-noise ratio (SNR) is measured at the receiver, the SNR information is fed back to the transmitter on a return channel, and the bandwidth and maximum data rate are selected at the transmitter. In U.S. Pat. No. 5,541,955, Adaptive Data Rate Modem, the data rate is adapted in a Trellis code encoder that maintains a constant channel symbol rate and a single signal set. Soft decision matrices are used in the receiver to provide an estimate of the signal-to-noise ratio that is sent back to the transmitter via a return channel. By using a relatively large signal set for all data rates, this technique would be vulnerable to multipath induced intersymbol interference at lower transmission rates.
The above techniques also do not address how to exploit transmit and receive diversity channels in an adaptive data rate system. Moreover, the above techniques use signal-to-noise ratio as a quality measure that may be inadequate in large multipath environments where the positive (implicit diversity) and negative (intersymbol interference) effects of multipath contribute to the optimization of transmitted data rate.